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In my domain (finance) correlations between vectors are unstable but (maybe) dependent on cross-sectional relationships in the problem space. Some of the mathem
by vegabook 11y ago
In my domain (finance) correlations between vectors are unstable but (maybe) dependent on cross-sectional relationships in the problem space. Some of the mathematics behind elastic body deformation (car tyres in in mechanical engineering, fluid dynamics in weather forecasting) have high applicability. Tensors are required.
It's true that tensors are hard to reason about - they overclock my brain most of the time - but there is no doubt that, just like moving from scalars to vectors massively increases your real-world modelling power, so does the natural extrapolation to matrices, and from there, tensors.
- pathsjs 11y agoIt's not that tensors are particularly hard to reason about. It's just that the way they are represented as multidimensional arrays hides very well the fact that they are element of a tensor product (hence tensors). Natural operations like, well, the tensor product are often not even available.
- vegabook 11y agoI agree that tensors are often used simply as a convenient representation for multiple lower-dimensional objects. I suspect that is because there is still plenty of value in many fields, including mine, in exploring scalar, vector, and matrix representations of problems, and tensors are often unexploited. They're used as convenient data structures, not as algorithmic necessities. Still, as more and more people have access to data and explore it, increasing competition, reducing the "alpha" of simpler analyses, moving deeper into dimensionality on algorithms will be the only choice for those who want to innovate, is my view. So it is probably necessary to have the tools at our disposal already.